# How do you graph f(x)=abs(x-3)+4?

Feb 5, 2015

Actually there are two graphs

$f \left(x\right) = \left(x - 3\right) + 4 = x + 1$
for all values of $x \ge 3$
and:
$f \left(x\right) = - \left(x - 3\right) + 4 = - x + 7$
for all values of $x \le 3$

The $x = 3$ is important, as at that point $x - 3$ becomes negative and must be "saved" by the abs-function.

At the value of $x = 3$ the two functions meet at $\left(3 , 4\right)$
graph{abs(x-3)+4 [-28.88, 28.85, -14.43, 14.45]}